1. Field of the Invention
The present invention relates to converting digital signals and, more particularly, to a method and apparatus for reducing errors in a digital signal played back from a recording medium.
2. Description of the Prior Art
The fidelity of a recorded signal can be greatly enhanced if the analog signal is converted to digital form prior to recording. A common recording scheme converts the original analog signal into digital data using pulse code modulation (PCM). The PCM digital data is then modulated using the NRZI (non-return to zero, inverted) coding system. The NRZI coding system enables recording at the same bit densities possible with NRZ coding but without the problems associated with signal polarity in NRZ coding.
In the NRZI coding system a "1" digital bit is represented by a transition between the two levels of a bi-level signal, while a continuation of the bi-level signal at the same level represents a "0" digital bit. In NZRI code, then, the actual level of the signal, whether high or low, does not represent digital information. Instead, the digital information is determined by whether or not the signal has changed levels between adjacent bit cells. For example, if the portion of the signal representing a particular bit of digital data is at the same level as the portion representing the preceding bit, then that particular bit is a digital zero.
A problem encountered particularly with magnetic tape recorders is their inherently poor reproduction of low frequency signals. Thus, when NRZI-coding is used, a series of digital zeros (represented by no level transitions in the signal) will be reproduced with reduced fidelity. Converting schemes are commonly used to convert the original or base digital signal into a larger number of digital bits. That way, additional digital ones, or level transitions in NRZI-code, can be artificially provided by selecting bit combinations that have no long periods between level transitions to represent the original digital signal. The present invention uses that approach, which is described in detail below.
Those converting schemes inherently increase the amount of tape required for recording a given amount of the base digital signal. Each base word is represented by a converted word having more bits, and the bit density of any recorded signal has an upper limit defined by the recording head size and the width of the track on the tape available for recording. The bit density can be increased only as long as the resulting decrease in the signal-to-noise (S/N) ratio of the reproduced signal enables reliable recovery of the recorded signal on playback. That problem is aggravated in portable tape recorders because recording head size is reduced to provide portability.
The S/N ratio can be increased by optimizing certain properties of the recorded signal, in particular the ratio between the "window margin", T.sub.w, and the "minimum length between transition", T.sub.min. T.sub.w represents the time required to read the information in any given part of the signal and T.sub.min is the time occupied by one bit of data in the signal. If T.sub.w /T.sub.min is made as small as possible, preferably lower than 2, then the S/N ratio can be maintained at a level that will enhance accurate reproduction. It is also desirable to minimize the ratio of T.sub.max /T.sub.min, where T.sub.max is the maximum time between level transitions. In an NRZI-coded signal, T.sub.max is determined by the number of consecutive zeros. As T.sub.max /T.sub.min becomes larger, the frequency of the recorded signal decreases, which affects the fidelity of the reproduced signal.
As for converting schemes, one prior art method for using a particular number of bits of digital data to provide a larger number is the Gabor code. It converts a combination of two bits of data (B.sub.1, B.sub.2) of a base signal into a three-bit combination (P.sub.1, P.sub.2, P.sub.3), according to the following formula: EQU P.sub.1 =P.sub.3p +B.sub.1 +B.sub.2 .times.B.sub.1f EQU P.sub.2 =P.sub.3p .times.B.sub.1 +B.sub.2 EQU P.sub.3 =P.sub.3p +B.sub.1 +B.sub.2
where p represents the information from the group of data just converted, f represents the information from the next group to be converted, and the bar indicates an inversion (from "0" to "1", or vice versa) of the particular bit with the bar.
The converted signal is restored according to these formulas: EQU B.sub.1 =P.sub.3p .times.P.sub.1p +P.sub.3p .times.P.sub.1 .times.P.sub.3 EQU B.sub.2 =P.sub.2 .times.P.sub.3
By using the Gabor code for the conversion, T.sub.2 =0.67T and T.sub.min =0.67T, (where T=the duration of the signal representing one bit) so that T.sub.w /T.sub.min =1. T.sub.max, when the converted signal is NRZI-coded, in the Gabor Code can be limited to 1.33T. The ratio of T.sub.max /T.sub.min is thus 2, which is small enough to enable accurate reproduction of the recorded signal.
Another converting system converts four bits into five bits. Five bits can be combined in 17 different ways in which no more than two digital zeros will ever appear together (either internally or from one 5-bit word to the next). Those 17 ways are the digital representations of the decimal numbers 9-11, 13-15, 18, 19, 21-23, 25-27 and 29-31. Since the original four bits can assume only 16 combinations, it is possible to use a 4/5 converting system to record in NRZI code such that no more than two digital zeros ever appear consecutively. Hence, in the 4/5 converting system, T.sub.w =0.8T, T.sub.min =0.8T and T.sub.max =2.4T when NRZI-coded. The ratio T.sub.w /T.sub.min is 1 and T.sub.max /T.sub.min =3, both of which provide adequate fidelity of the reproduced signal.
Another problem encountered in digital signals recording results from the fact that a DC signal cannot be recorded or reproduced accurately. With NRZI-coding, detection of the location of the changes between the high and low levels of the signal is critical to accurate recovery of the digital data. But since the DC level of the signal is lost in recording, level changes in the reproduced signal cannot in many cases be accurately determined. Neither of the converting schemes described above, the 2/3 Gabor code scheme and the 4/5 scheme, lends itself to accurate recovery of the information because of problems in determining the proper DC level to use in detecting signal level changes.
U.S. Pat. No. 4,387,364, which is assigned to the assignee of the present invention, describes a technique for overcoming that problem which is useful with NRZ coding. While that technique is effective for NRZ coding, it does not disclose a solution to the same problem when NRZI coding is used. In addition, the disclosed technique results in a signal with a T.sub.max /T.sub.min ratio that is high enough to increase the possiblity that distortion will occur when the signal is played back.
Converting systems are known which convert 24 bits into 30 bits or 16 bits into 20 bits and which enable accurate recovery of level transitions in the signal. Both of those systems have practical problems. The number of bits required to effect the conversion is excessive, as is the number required to restore the original signal. The converted signal has enough additional bits that the length of recording medium is greatly increased. The apparatus required to carry out those converting systems thus becomes unduly large and complex.